Question 1

Fraction Analogy — “1/9 : 1/81 :: 3/13 : ?”. Detect the pattern that maps the first fraction to the second and apply it to 3/13.

Accepted Answer

Introduction / Context: Fraction analogies often involve transformations on the numerator, denominator, or both. The pair “1/9 : 1/81” suggests a rule that holds the numerator fixed at 1 while transforming the denominator in a specific way. We must discover that transformation and then apply it to “3/13.” Given Data / Assumptions: The first numerator is 1 and remains 1 in the mapped fraction. The denominator changes from 9 to 81. We seek a consistent transformation that we can apply when the left fraction is 3/13. Concept / Approach: Notice 81 = 9^2. A clean rule is: map a/b → 1/b^2 (fixing the numerator at 1 and squaring the denominator). This reproduces 1/9 → 1/81 exactly. Applying the same rule to 3/13 gives 1/13^2 = 1/169. Step-by-Step Solution: Identify pattern: denominator squared while numerator becomes 1 (a/b → 1/b^2).Apply to 3/13: denominator 13 → 13^2 = 169; numerator resets to 1.Result: 1/169. Verification / Alternative check: Alternative interpretations like dividing by 9 (1/9 → 1/81 because (1/9)/9 = 1/81) fail for 3/13 because (3/13)/9 = 3/117 (not among standard simplest forms and generally not offered). The denominator-square rule works perfectly and yields an offered option. Why Other Options Are Wrong: 1/125, 1/120, 1/127 — denominators do not equal 13^2; arbitrary.3/117 — would fit a “divide by 9” rule, but that rule is not suggested by the given pair in a standard way for fractions; the canonical pattern is denominator squared with numerator set to 1. Common Pitfalls: Overfitting a single arithmetic tweak (like division by a constant) when a clean structural transformation (denominator squared) more directly explains the example. Final Answer: 1/169

Question 2

Analogy — “Sheep : mutton :: Deer : ?”. (Recovery applied: corrected spelling from “Dear” to “Deer”; standardized meat term.)

Accepted Answer

Introduction / Context: This is a standard animal-to-meat analogy. “Sheep : mutton” names the animal and the conventional culinary name of its meat. We must select the culinary meat term that corresponds to “deer.” A minor Recovery-First adjustment is applied: the stem contained “Dear,” which is corrected to “Deer” to preserve the intended meaning. Given Data / Assumptions: “Mutton” is the culinary name of sheep meat. The goal is to find the established culinary name of deer meat. We ignore generic words like “meat/flesh” and unrelated species’ meat terms. Concept / Approach: Deer meat is called “venison.” The relation is animal → culinary term for its meat. The correct answer should be that widely accepted culinary label. Step-by-Step Solution: Map the relation: sheep → mutton; deer → venison.Eliminate generic or incorrect terms (meat, flesh, veal, beef).Select “venison.” Verification / Alternative check: “Veal” is calf (young cattle) meat; “beef” is adult cattle meat. “Meat/flesh” are generic and do not parallel the specific culinary naming pattern seen in “mutton.” Why Other Options Are Wrong: meat / flesh — generic nouns; not culinary-specific.veal — meat from calves, not deer.beef — meat from cattle, not deer. Common Pitfalls: Choosing a generic or familiar meat term rather than the exact culinary label that fits the species in the stem. Final Answer: venison

Analogy Questions